BPS spectra from BPS graphs

Abstract

I present a simple graphical method to find the BPS spectra of $A_1$ theories of class S. BPS graphs provide a bridge between spectral networks and BPS quivers, the two main frameworks for the study of BPS states. Here I show how to essentially read off from a BPS graph the quantum spectrum generator (or BPS monodromy), expressed as a product of quantum dilogarithms. Thanks to the framed wall-crossing phenomenon for line defects, the determination of the BPS spectrum reduces to the computation of quantum parallel transport across the edges of the BPS graph.

17 pages, 12 figures

References in corpus (5)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• R-Twisting and 4d/2d Correspondences
• Quantum Holonomies from Spectral Networks and Framed BPS States
• Spectral Networks and Snakes
• Wall-Crossing Invariants from Spectral Networks